Abstract
Let R be a prime ring and set [x, y]1 = [x, y] = xy - yx for x, y ∈ R and inductively [x, y]k = [[x, y]k-1, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.
Original language | English |
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Pages (from-to) | 259-270 |
Number of pages | 12 |
Journal | Monatshefte fur Mathematik |
Volume | 158 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2009 Jan 1 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)